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SageMath
E = EllipticCurve("cj1")
E.isogeny_class()
Elliptic curves in class 108900cj
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
108900.v2 | 108900cj1 | \([0, 0, 0, -117975, 17756750]\) | \(-4253392/729\) | \(-31123310724000000\) | \([]\) | \(870912\) | \(1.8911\) | \(\Gamma_0(N)\)-optimal |
108900.v1 | 108900cj2 | \([0, 0, 0, -9918975, 12023981750]\) | \(-2527934627152/9\) | \(-384238404000000\) | \([]\) | \(2612736\) | \(2.4404\) |
Rank
sage: E.rank()
The elliptic curves in class 108900cj have rank \(0\).
Complex multiplication
The elliptic curves in class 108900cj do not have complex multiplication.Modular form 108900.2.a.cj
sage: E.q_eigenform(10)
Isogeny matrix
sage: E.isogeny_class().matrix()
The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the Cremona numbering.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.